Notes:

Summary plots - Sample strategy is on the y-axis and number of sites is on the x-axis. Each plot is paired by parameter level vertically and the values in the cells are the mean value across all of the simulations for that parameter level. Note that each average encompasses all of the other varying simulation parameters.

Full plots - Sample strategy is on the y-axis and number of sites is on the x-axis. Each plot represents a unique simulation and the values in the cells are the mean value across all of the 10 iterations of that simulation across all three unique landscape seeds (i.e., all three sets of Neutral Landscape Models) for a total of 30 replicates. For these plots: K = population size (not to be confused with the number of latent factors (K)), phi = selection strength, m = migration, H = spatial autocorrelation, r = correlation between environmental layers.

RAE - Ratio Absolute Error - is the absolute difference between the observed and expected estimate of the ratio of IBE to IBD (i.e. the coefficient of IBE divided by the coefficient of IBD)

Bias - bias was calculated by taking the mean difference between the observed and expected coefficients or ratios

1. MMRR

1.1 Individual sampling

1.1.1 Summary plots

1.1.2 Linear mixed effects models

RAE

Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number -0.0004 12.5300 12.5300 1 15.3480K 1859.075494 0.0***
Population size 0.0137 0.7175 0.7175 1 15.3480K 106.451353 7.1 × 10-25***
Migration 0.0633 15.3874 15.3874 1 15.3480K 2283.024663 0.0***
Selection strength -0.0044 0.0747 0.0747 1 15.3480K 11.078001 8.8 × 10-4***
Spatial autocorrelation -0.0028 0.0293 0.0293 1 15.3480K 4.345606 0.037**
Environmental correlation 0.0024 0.0224 0.0224 1 15.3480K 3.319423 0.068
*** p < 0.001
** p < 0.05
Contrast Estimate SE Z ratio p
EG - G 0.0048 0.0019 2.5787 0.04872657
EG - R 0.0074 0.0019 3.9678 4.2 × 10-4
EG - T -0.0243 0.0019 -12.9557 0.0
G - R 0.0026 0.0019 1.3891 0.50617245
G - T -0.0291 0.0019 -15.5345 0.0
R - T -0.0317 0.0019 -16.9235 0.0

1.1.3 Full plots

RAE

Ratio Bias

IBD Bias

IBE Bias

1.2 Site sampling

1.2.1 Summary plots

1.2.2 Linear mixed effects models

RAE

Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number -0.0081 24.3823 24.3823 1 8.6290K 1053.036286 4.6 × 10-218***
Population size 0.0078 0.1306 0.1306 1 8.6290K 5.642233 0.018**
Migration 0.0398 3.4168 3.4168 1 8.6290K 147.567328 1.1 × 10-33***
Selection strength -0.0150 0.4889 0.4889 1 8.6290K 21.114952 4.4 × 10-6***
Spatial autocorrelation -0.0415 3.7215 3.7215 1 8.6290K 160.727252 1.7 × 10-36***
Environmental correlation 0.0164 0.5808 0.5808 1 8.6290K 25.084085 5.6 × 10-7***
*** p < 0.001
** p < 0.05
Contrast Estimate SE Z ratio p
EG - EQ -0.0035 0.0040 -0.8847 0.6499763
EG - R 0.0128 0.0040 3.1916 4.0 × 10-3
EQ - R 0.0163 0.0040 4.0763 1.4 × 10-4

1.2.3 Full plots

RAE

Ratio Bias

IBD Bias

IBE Bias

2. GDM

2.1 Individual sampling

2.1.1 Summary plots

2.1.2 Linear mixed effects models

RAE

Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number -0.0003 9.4335 9.4335 1 15.3430K 8.826316e+02 1.2 × 10-188***
Population size 0.0231 2.0533 2.0533 1 15.3430K 1.921097e+02 2.0 × 10-43***
Migration 0.0799 24.4973 24.4973 1 15.3430K 2.292047e+03 0.0***
Selection strength -0.0003 0.0002 0.0002 1 15.3430K 2.244788e-02 0.88
Spatial autocorrelation 0.0020 0.0153 0.0153 1 15.3430K 1.435012e+00 0.23
Environmental correlation -0.0057 0.1237 0.1237 1 15.3430K 1.157134e+01 6.7 × 10-4***
*** p < 0.001
Contrast Estimate SE Z ratio p
EG - G -0.0135 0.0024 -5.7327 5.9 × 10-8
EG - R -0.0097 0.0024 -4.0895 2.5 × 10-4
EG - T -0.0198 0.0024 -8.3745 4.1 × 10-14
G - R 0.0039 0.0024 1.6429 0.35443857
G - T -0.0062 0.0024 -2.6417 0.04111055
R - T -0.0101 0.0024 -4.2845 1.1 × 10-4

2.1.3 Full plots

RAE

Ratio Bias

IBD Bias

IBE Bias

2.1.4 Failed fits

Occasionally GDM fails to fit a model, in which case an NA value is assigned. Here we visualize the proportion of NAs (i.e., cases of failed fit) across the simulations:

Proportion of failed models:

2.2 Site sampling

2.2.1 Summary plots

2.2.2 Linear mixed effects models

RAE
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number -0.0064 14.4681 14.4681 1 8.3500K 5.407432e+02 5.9 × 10-116***
Population size 0.0000 0.0000 0.0000 1 8.3500K 2.777680e-05 1.00
Migration 0.0231 1.1117 1.1117 1 8.3500K 4.155104e+01 1.2 × 10-10***
Selection strength -0.0049 0.0503 0.0503 1 8.3500K 1.879243e+00 0.17
Spatial autocorrelation 0.0007 0.0009 0.0009 1 8.3500K 3.448557e-02 0.85
Environmental correlation -0.0137 0.3905 0.3905 1 8.3500K 1.459672e+01 1.3 × 10-4***
*** p < 0.001
Contrast Estimate SE Z ratio p
EG - EQ -0.0760 0.0044 -17.3557 0.0
EG - R -0.0272 0.0044 -6.1624 2.1 × 10-9
EQ - R 0.0488 0.0044 11.1986 7.3 × 10-15

2.2.3 Full plots

RAE

Ratio Bias

IBD Bias

IBE Bias

2.2.4 Failed fits

Occasionally GDM fails to fit a model, in which case an NA value is assigned. Here we visualize the proportion of NAs (i.e., cases of failed fit) across the simulations:

Proportion of failed models:

NOTES: - problem: inferences across all simulations are different from that of a single simulation - average across all simulation also don’t make sense - but we care about what is true across them all in some sense because that is the info we can go off of, not the “best case scenario” - however the average of them all assumes that the simulations cover all of parameter space as a meaningful summary - fuck i don’t care about any of this - what is significant varies based on sample size - sample size is treated as continuous - do I need to run more simulations to get more power?

  • NOTE: figure out how to describe bias patter (underestimation for grid only occurs under certain scenarios)